Analysis & PDE
- Anal. PDE
- Volume 10, Number 2 (2017), 323-350.
Operators of subprincipal type
In this paper we consider the solvability of pseudodifferential operators when the principal symbol vanishes of at least second order at a nonradial involutive manifold . We shall assume that the subprincipal symbol is of principal type with Hamilton vector field tangent to at the characteristics, but transversal to the symplectic leaves of . We shall also assume that the subprincipal symbol is essentially constant on the leaves of and does not satisfying the Nirenberg–Trèves condition () on . In the case when the sign change is of infinite order, we also need a condition on the rate of vanishing of both the Hessian of the principal symbol and the complex part of the gradient of the subprincipal symbol compared with the subprincipal symbol. Under these conditions, we prove that is not solvable.
Anal. PDE, Volume 10, Number 2 (2017), 323-350.
Received: 23 November 2015
Revised: 18 September 2016
Accepted: 1 November 2016
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35S05: Pseudodifferential operators
Secondary: 35A01: Existence problems: global existence, local existence, non-existence 58J40: Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx] 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx]
Dencker, Nils. Operators of subprincipal type. Anal. PDE 10 (2017), no. 2, 323--350. doi:10.2140/apde.2017.10.323. https://projecteuclid.org/euclid.apde/1510843424